One's favourite American drive (7)
I believe the answer is:
impetus
'drive' is the definition.
(impetus is a kind of drive)
'one's favourite american' is the wordplay.
'one's' becomes 'im' ('one is' is a formal way of saying 'I am').
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'american' becomes 'us'.
'im'+'pet'+'us'='IMPETUS'
(Other definitions for impetus that I've seen before include "Catalyst" , "Driving force, momentum" , "Moving force" , "influence" , "Incentive, stimulus" .)